Elementary tolerance analysis with nonlinear assembly equations or functions can lead to significant errors when either Worst Limits or Root Sum Squares are applied. A previous paper [1] presented the errors and a corrective design method for Worst Limit elementary tolerance analysis. In this paper, Root Sum Squares tolerance analysis is applied to a nonlinear assembly equation, which gives significant errors in the assembly acceptance fraction. Advanced statistical analysis can be used in an iterative design procedure to specify the independent variables which meet the specified assembly in spite of the nonlinearities.